Stability and Control Analysis

INTRODUCTION

When designing a helicopter for good performance, the engineer deals almost entirely with laws of physics that are reasonably constant and more or less well understood. When designing for good stability and control, on the other hand, the engineer must also deal with the capabilities of pilots, which are variable and are only partially understood. The problem becomes one of machine-man matching. If the characteristics of the machine are not matched to the natural capabilities of the man, either the machine cannot be operated or the capabilities of the man must be upgraded by training. One example of the problem is the difference between the training and talent required to successfully ride a tricycle, a bicycle, and a unicycle. In this case, the increasing ability required is due primarily to the progressive deterioration in stability. Another example is the difference between attempting a docking maneuver with rowboat, a cabin cruiser, and an ocean liner. In this example, instability is no problem, but the ability to generate accelerations in the required directions becomes more and more degraded until, in the case of the ocean liner, the ability to dock without doing damage is completely inadequate and the job must be relinquished to tugboats.

Thus there are two important elements in machine-man matching: stability and response to control inputs. The best machine-man matching in the aircraft field involves an aircraft that simultaneously has high stability and a rapid and positive response to the pilot’s control inputs. Many early helicopters were not good examples of machine-man matching. In general, a helicopter without special stability augmentation provisions not only is unstable, but its response to control inputs is slow, with maximum results appearing some time after the pilot starts the control input. These characteristics give the pilot a combination of fear of the instability and impatience with the slow response. In many cases the student pilot overcontrols and actually finds himself contributing to the instability rather than damping it. A classic remark made by a student following his first attempt to hover was, "It’s like riding a pogo stick over a floor covered with greasy ball bearings.” Fortunately, pilots an be trained to fly even unstable helicopters and at the same time, the helicopter itself can be tamed by various means.

DEFINITIONS

Stability is the tendency of an object to return to its original conditions following a disturbance. A marble in a bowl is stable, but a marble balanced on top of an inverted bowl is unstable since once disturbed it will go away from its original position with ever increasing speed. The in-between case is a marble on a flat plate, which has no tendency either to return or to leave: it is thus neutrally stable. Static stability is measured by the force or moment per unit of displacement that acts to restore the object to its original position. Dynamic stability is measured by the time required to return to its original position following a unit displacement. The stability characteristics of a system can be categorized by the type of time history it has following a displacement. Figure 9.1 shows six types of time histories characteristic of aircraft.

Control is the ability to apply forces and moments to the aircraft to maintain it in a steady flight condition in gusty air or to perform a desired maneuver. Two terms are used to define control further: control power is the measure of the total moment or force available to the pilot for maneuvering from a steady trimmed flight condition or for compensating for large gust disturbances; control sensitivity is the measure of either aircraft acceleration or steady velocity produced by a unit of control motion. It is of importance in defining the precision of control.

A situation that exists in almost all types of aircraft is that increased stability of the basic airframe results in decreased controllability. As a general rule, pilots prefer controllability over stability, since it permits them to get out of tight spots that even very stable aircraft might get into. In this, they are following the lead of the Wright Brothers, whose "Flyer” was very unstable but also very controll­able.